Application of Exponential-Based Methods in Integrating the Constitutive Equations with Multicomponent Nonlinear Kinematic Hardening

Rezaiee‐Pajand, Mohammad; Nasirai, Cyrus; Sharifian, Mehrzad

doi:10.1061/(asce)em.1943-7889.0000192

Cited by 23 publications

(3 citation statements)

References 24 publications

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“…Associated with the well-known radial return mapping in stress integration presented by Wilkins [58], many research subjects such as consistent tangent operator, iso-error map, and integration stability were studied [59][60][61]. Recently introduced exponential map based stress integration schemes showed their robustness [62][63][64][65]. However, these studies were hardly utilized to overcome the non-convergent issues in YPP applications.…”

Section: Stress Integration Algorithmsmentioning

confidence: 99%

Computational Studies for the Yield-Point Phenomenon of Metals

Kim

2020

Multiscale Sci. Eng.

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The yield-point phenomenon (YPP) is an accustomed topic in sheet metal forming fields. Over hundred and fifty years since the first observation of the YPP, many research efforts have been continued to understand and describe it. Recent spotlights for the YPP studies are focusing on high-degree numerical methods with the support of increasing computing performance. Here, we review the representative computational studies on YPP to share the latest progress and remaining challenges to obtain better mechanical insights into it. After the duality of the YPP is addressed in terms of avoiding and utilizing it, the constitutive material models for the YPP as well as bake hardening models are discussed for a continuum level FE simulations, and the features of the discussed YPP models are compared. Microscopic and multiscale schemes are also briefly handled. It is expected that more advanced computational work can be initiated from this review.

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Section: Stress Integration Algorithmsmentioning

confidence: 99%

Computational Studies for the Yield-Point Phenomenon of Metals

Kim

2020

Multiscale Sci. Eng.

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“…They also developed two exponential map integrations for Drucker–Prager plasticity. Moreover, the exponential map method was advanced by Rezaiee-Pajand et al (2010, 2011, 2014a, 2014b) for cyclic plasticity models comprising von-Mises yield function along with nonlinear kinematic hardening laws of Chaboche (1986), Ohno and Wang (1993) and Abdel-Karim and Ohno (2000). Considering the pressure-sensitive material’s elastoplastic behavior, the Drucker–Prager yield surface along with the mixed hardening was take into account to propose the angels based integrations by Rezaiee-Pajand and Sharifian (2012) and Rezaiee-Pajand et al (2014a, 2014b).…”

Section: Introductionmentioning

confidence: 99%

A hybrid method to update stress for perfect von-Mises plasticity coupled with Lemaitre damage mechanics

Tavoosi

Sharifian

2019

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Purpose The purpose of this paper is to suggest a robust hybrid method for updating the stress and plastic internal variables in plasticity considering damage mechanics. Design/methodology/approach By benefiting the properties of the well-known explicit and implicit integrations, a new mixed method is derived. In fact, the advantages of the mentioned techniques are used to achieve an efficient integration. Findings The numerical studies demonstrate the high precision and robustness of the suggested algorithm. Research limitations The perfect von-Mises plasticity together with Lemaitre damage model is considered within the realm of small deformations. Practical implications Updating stress and plastic internal variables are of utmost importance in elastoplastic analyses of structures. The accuracy and efficiency of stress-updating methods significantly affect the final outcomes of nonlinear analyses. Originality/value The idea which is used to derive the hybrid method leads to an efficient integration method for updating the constitutive equations of the damage mechanics.

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“…A numerical integration based on exponential maps for the Drucker-Prager's elastoplastic models was presented by Rezaiee-Pajand and Nasirai (2008). Rezaiee-Pajand et al (2010) proposed an exponential-based scheme in integrating the constitutive equations along with multi-component nonlinear kinematic hardening. Finally, Rezaiee-Pajand et al (2011) derived an accurate solution and two exponential-based integrations for Drucker-Prager plasticity with linear mixed hardening.…”

Section: Introductionmentioning

confidence: 99%

Integration of nonlinear mixed hardening models

Rezaiee‐Pajand

Nasirai

Sharifian

2011

Multidiscipline Modeling in Materials and Structures

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Purpose -The purpose of this paper is to present a new effective integration method for cyclic plasticity models. Design/methodology/approach -By defining an integrating factor and an augmented stress vector, the system of differential equations of the constitutive model is converted into a nonlinear dynamical system, which could be solved by an exponential map algorithm. Findings -The numerical tests show the robustness and high efficiency of the proposed integration scheme.Research limitations/implications -The von-Mises yield criterion in the regime of small deformation is assumed. In addition, the model obeys a general nonlinear kinematic hardening and an exponential isotropic hardening. Practical implications -Integrating the constitutive equations in order to update the material state is one of the most important steps in a nonlinear finite element analysis. The accuracy of the integration method could directly influence the result of the elastoplastic analyses. Originality/value -The paper deals with integrating the constitutive equations in a nonlinear finite element analysis. This subject could be interesting for the academy as well as industry. The proposed exponential-based integration method is more efficient than the classical strategies.

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Application of Exponential-Based Methods in Integrating the Constitutive Equations with Multicomponent Nonlinear Kinematic Hardening

Cited by 23 publications

References 24 publications

Computational Studies for the Yield-Point Phenomenon of Metals

Computational Studies for the Yield-Point Phenomenon of Metals

A hybrid method to update stress for perfect von-Mises plasticity coupled with Lemaitre damage mechanics

Integration of nonlinear mixed hardening models

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